Stupid questions thread then.
Can someone help me understand why matrices are so great?
What am I missing here?
>>8056620
http://www.benfrederickson.com/matrix-factorization/
(i haven't actually read that image, but here's some cool applications of matrices)
I can't fucking study
I always
open 4chan
open social media
open porn
open youtube
FUCK
>>8056624
Go study somewhere without a computer then
>>8056620
Best thing?
Solving large systems of equations
For example, a truss in static equilibrium generates 3 equations for each member and a common problem (in class) would have something like 7-8 members.
So you end up with 21-24 equations you need to solve for to get forces and thus stress.
Plugging it into a matrix makes it algorithmic, instead of solving for each unknown individually by plugging and manipulating algebra.
>>8056625
Except I need my computer to study. What I need and I don't have is self-control and self-discipline
>>8056634
>people never studied before computers
learn how to do calculations by hand and find books in the library by walking around you fucking degenerate moron. you really think von neumann needed a fucking macbook to design eniac? no he just had to get a carbon copy turing's. no macbook necessary.
>>8056620
Any linear map between finite dimensional vector spaces can be completely determined by a list of numbers, from which we can glean lots of information about eigenvalues, injectivity, etc. very easily. I'd say that's pretty great.
>>8056632
>20-something
>large
Try millions or tens of millions in harmonic analysis of a structure like a rocket
>>8056665
Essentially this. When you can reduce the study of a complex object (linear maps between finite dimensional vector spaces) to some numbers, you can say it's a great success in math. In addition:
> a particularly interesting case of this are base changes (where the matrix is invertible)
> this includes geometric manipulations (f.e. rotations)
> apart from all of this, programs run a lot faster when they do their operations in matrices instead of 1 by 1.
What happened between these two steps?
>>8056621
>>8056632
>>8056665
I can see how matrices would be useful in engineering and that.
But the specific example of matrices I want to know about it the matrices used by graphics processing units. GPUs are specifically designed to accept and operate on matrices because apparently it's faster? But I can't see how, hence the OP picture.
>>8056706
Distributive property?
>>8056706
They just collected the terms
What does it mean for a matrix to be positive semidefinite?
>>8056851
If M is your matrix, [math] |x \rangle [/math] any vector and [math] \langle x | [/math] its covariant representative, then
[math] \langle x | M |x \rangle \geq 0 [/math]
Why haven't we talked about exotic particles yachting negative mass imaginary mass God particle
>>8056672
Its just an example dude.
>>8056708
GPUs use matrices for intense lighting calculations.
I haven't implemented them myself, but I remember reading something about orienting vectors (like that object is at 0,0,2 from the player) via matrix multiplication
You can use them for any system of finite linear equations.
To find the equation of the line that best "fits" a bunch of data points (minimises MSE for instance) -- do you always have to do the thing with linear regression? Is there no closed form formula that just gives me the coefficients?
>>8056654
Not him but for many of my classes the homework and all that is done online through some portal so you're required to have a computer
We use matrices to plot tensors in stress analysis
Recently I was trying to find the expected value of a matrix with restricted row and column sums. The method I devised involves solving for the hypervolume of an (m-1)(n-1) dimensional polytope, which involves solving a large amount of nested integrals. Is there an easier way to do this?
>>8056973
>highschool
What contents should I know before Calculus?
>>8056620
go study first.
let's talk again in 3 years.
Matrices just map from one vector to another, without leaving the corresponding vectors space. This can then be specialized to a great many things in any field of science, even the shitty soft ones.
>>8056634
>Except I need my computer to study
Why?
>>8057190
Functions, sets, polynomials
I have a 17 year old nephew who doesn't care about high school and just created a twitch account where he thinks he's gonna be rich. The kid has five Fs this semester and he averages 3 failed classes per semester since 9th grade. My nephew will be 18 in February. What is there to do with him?
>>8057419
it will suck in the short term (only a few years, if you're lucky) but you probably just have to let him have his journey and figure it out
if he can't figure it out on his own then there is no hope and nothing to be done, so don't worry about it at that point
if he can figure it out on his own then it will be all the sweeter and more beneficial for the rest of his life
and by figure it out on his own i mean realize that there's more to life than video games and he's likely just wasting his prime years away, and that he should probably do more with his years.
notice all the probablys and maybes? Maybe this is his path. Whatever. He'll figure it out. Or he won't. Either way is something he has to do - not something you can force.
So I have been told that, if f is derivable in x, [math]\lim_{h\to 0} \frac{f(x+h)}{h}-f'(x)=0[/math], but I can't figure out how to prove it. How do I do it, /sci/?
>>8057419
It's a shit reality but the other anon is right. If you think you have a shot in hell of trying to tell a teenager what to do, you've forgotten what it's like to be a teenager.
If he wants to fuck his life up you can't stop him. Best you can do is be available to help if/when he decides to fix it.
>>8056708
okay, you scaled the cube which is orthogonal to all the axes of your space. Now try turning it.
>>8057449
The first term is the definition of the derivative of f at x. The second term is the derivative of f at x. You're literally subtracting two things that are by definition the same (assuming, as here, that f'(x) exists).
>>8057550
It's the limit of the whole expression, [math]\lim_{h\to 0} [\frac{f(x+h)}{h} - f'(x)][/math].
Does it make sense like that?
>>8057572
Doesn't matter, the f'(x) is independent of h, so it pops out of the limit. The first term should be [f(x+h)-f(x)]/h as h->0 to make the expression a valid equation.
>>8057575
You are right, turns out the person who told me skipped the-f(x) by mistake.
Thank you.
I have an overkill PC that doesn't hit 30% no matter what I do. Any programs that can take advantage of the processing power whilst teaching me a thing or two? Like protein structure simulation or something to that effect (for free)?
How do I show [math] \langle \mathbb{R}, + \rangle [/math] is isomorphic to [math] \langle \mathbb{R}^{+}, \cdot \rangle [/math] with [math] \phi : \mathbb{R} \to \mathbb{R}^{+}[/math] defined by [math]\phi(x) = 2^{x}[/math]? I know i have to show one-to-one, onto and [math] \phi(a + b) = \phi(a) \cdot \phi(b) [/math]. I just don't know how i would show these things. (first abstract algebra class, if that matters)
Has anyone used Engineering Mechanics by RC Hibbeler? Is it good?
>>8057809
>I know i have to show one-to-one, onto
The explicit inverse is incredibly easy to state.
>>8056708
https://acko.net/tv/webglmath/
>>8057809
To show one to one, you need to show EITHER:
f(a) = f(b) implies a = b
OR
a != b implies f(a) != f(b)
This is easy, though.
Suppose f(a) = f(b).
Then, 2^a = 2^b.
Take the log_2 of both sides.
That tells you a = b. Right? If two powers of 2 are equal, then their exponents need to be the same.
To show onto?
You need to show that any element in R+ is mapped to by some element of R by your map. So, take b in R+. If you want b = 2^x, what element of R maps to it? Well, I think it is log_2(b). Notice that this is OK because everything in R+ is positive.
>>8057812
Pretty good, but if you like theory should complement with some other books like Beer that you can find easily
>>8057839
so for onto, it would be: Let [math] b = 2^{x}, b \in \mathbb{R}^{+} [/math]. Since [math]\log_{2} b \in \mathbb{R}[/math], [math]\mathbb{R}[/math] and [math]\mathbb{R}^{+}[/math] are onto.
??
OP's picture:
> Guns are terrible compared to spoons as a tool to eat yogurt. Guns are therefore a terrible weapon.
Dude...
Hey guys, >>>/3/ here.
I'm planning on modeling atom representations for all (or the most I can) elements based on the Schrodinger's equation. I've come across a few, mainly the hydrogen one, but for the heavier elements I haven't had much luck. They seem fairly easy to design 3D-wise, and I want to do molecules at some point too if possible, so I was hoping if I could get some input from you guys since my knowledge of chemistry and quantum physics isn't that extensive.
>>8057839
>To show one to one, you need to show EITHER:
>
>f(a) = f(b) implies a = b
>
>OR
>
>a != b implies f(a) != f(b)
They're groups -- he just needs to show that only 0 maps to 1.
>>8057880
For multi-electron atoms you need to solve the Schrodinger equation numerically, I'm not very well versed in molecular modeling, but Google it and you'll find some better references then I could give you.
>>8057007
>ivy league university
>>8056620
In the OP:
How are you forming your matrix?
How are you multiplying your matrices?
You want to scale a cube, a shape in R3, but in your matrix, you have 4, 6 dimensional vectors, or 4 6-tuples. Then, when multiplying them, you have a 4x6 matrix multiplied by a 4x4 matrix.
I understand that 3*8=4*6, but you can't just shift around the number of components in each vector. Moreover, when scaling a matrix, we don't multiple by the scalar times the identity matrix, we just multiply our original matrix by a scalar.
If you want to learn why matrices are so great, go read up on them first. Grab a linear algebra book and start working through it. It's well worth your time.
If this is a troll, however, well done. 10/10, you got me.
>>8057851
or is it: Let [math]a \in \mathbb{R}, b \in \mathbb{R}^{+}[/math]. Suppose [math]\phi(a) = b[/math]. So [math]2^{a} = b[/math], [math]\log 2^{a} = \log b[/math], [math]a \log 2 = \log b[/math], [math]a = \frac{\log b}{\log 2}[/math]. So [math]a[/math] maps to [math]\frac{\log b}{\log 2}[/math]. Thus, they are onto. [math]\blacksquare[/math] ... ?
>>8057629
Are you me?
>>8057922
Wait, so all those shapes from the pic I posted correspond to the hydrogen atom? I don't get it, how does the electron cloud vary so wildly with just 1 electron? Forgive my ignorance, anon.
>>8057959
>How are you forming your matrix?
>How are you multiplying your matrices?
The matrix is formed by lining up the eight vertices vertically.
The vertices have 3 dimensions plus the homogeneous coordinate, so 4 dimensions total. It is actually 8 4-tuples
Again, I specifically wanted to know why matrices are good for graphics processing, hence taking into consideration the homogeneous value plus forming the matrix like a graphics processor would.
>>8058192
I should have used values other than 1 and -1 to make it more clear
>>8057935
>lying
>>8058020
Spherical harmonics are a hell of a thing.
>>8056708
For computer graphics, many operations to produce images are just vector arithmetic, scaling, skewing, reflecting, etc... Can all be handled by simple mathematical operations on points to find new transformed points.
So you end up with a system of linear equations to solve, and matrix algebra gives you a really easy and computationally efficient way to solve them.
Since I'm here. I'll ask this. Being /sci/ I might not be crowned immortal emperor of autism.
I want to track some life-success metrics in order to motivate and monitor myself through an irregular polygon. You might have seen it in fighting games, or similar places.
The final result would be an irregular polygon. Besides the distance to the vertices ('score' of each particular metric), I'd like to calculate the area, as some sort of general 'score' of how well I'm doing.
I'm not looking for advice in how to implement it, but about how to assign the 'stats' or 'skills' to each vertex so the area ('score') reflects something meaningful.
i.e. Assign stats that have low or zero synergy aligned and those that complement well with each other forming an angle close to 90º.
Chances are I haven't explained myself very well, but if you could help me out, I'd appreciate it. Ask for clarification if I'm not making much sense.
Is the Laplace operator a functional?
What else could be added for carbon fibers for different effects? I know the carbon fibers on a plane have an oxidize surface, with an epoxy layer. But carbon fibers are composites, so what else would be added?
Is it a secret?
>>8058470
Nope, since it maps one function onto another, not unto a scalar
When convoluting a harmonic signal with a finite impulse response, do I take harmonic represented by a frequency of 1*fundf as corresponding with the unit impulse of [eqn]\delta[n][/eqn]?
>>8058470
see 13:00
https://www.youtube.com/watch?v=sZ2qulI6GEk#t=60
>>8058707
I'm sorry I can't understand your question.
Can you elaborate? It seems some notions are lost in translation
Any good starting materials on wavelets?
>>8056620
The following was a question for an abstract algebra exam. I have no idea how to solve it, wondering if anyone knows how to prove it:
Let [math]\langle G, * \rangle[/math] be a group, and for any elements [math]a, b, c \in G[/math], show that the equation [math]a * x * b = c * a[/math] has a unique solution, and find such solution.
Matrices are fantastic.
They can simplify systems of differential equations, they can let you take derivatives without actually taking derivatives, they let you do complicated transforms easily, etc.
Basically, if you can find an isomorphism between the set you're working in and a set of matrices, you can simplify many problems into a set of matrix operations.
>>8060004
suppose [math]a*x*b=c*a[/math] has two solutions for [math]x[/math], [math]e[/math] and [math]f[/math]
substituting we see [math]a*e*b=a*f*b[/math], using left and right cancellation laws, [math]e=f[/math]
the solution is [math]a^{-1}*c*a*b^{-1}[/math]
alright, for people who know combinatorics:
i want to tile a 2xn set of spaces with tiles, which are 2x1 and 1x2 in size.
now, our a0 terms and a1 terms both cannot be tiled. does that mean a0=0 and a1=0?
>>8060040
oops, i mistyped the problem.
the spaces are 1xn, and our tiles are 1x2 and 1x3. just wondering what the a0 and a1 terms are.
>>8060037
i thought the solution was suppose to be what the binary operation actually was, so it should be manipulated like this:
[math]\begin{align*}a * x * b &= c * a \\ a^{-1} * a * x * b &= a^{-1} * c * a \\ x * b & = a^{-1} * c * a \\ x * b * b^{-1} & = a^{-1} * c * a * b^{-1} \\ x &= a^{-1} * c * a * b^{-1} \end{align*}[/math]
>>8060052
that's basically how i calculated the solution, showing uniqueness requires using the theorem regarding left and right cancellation
>>8060059
im pretty sure she assumes we can prove cancellation law anyway, so i could probably just put by cancellation law and thatd be enough. thanks
[math] \text { prop } [/math] Let [math] A [/math] be bounded above such that [math] s = Sup ( A) [/math] exists. Then [math] s \in \bar { A } [/math].
[math] \text { Proof } [/math] If [math] s \in A [/math] then there is nothing to prove, so suppose that [math] s \not \in A [/math] then let [math] \left ( x_n \right ) [/math] be a sequence in [math] A [/math] then [math] Sup ( A ) - 1/n \leq x_n \leq Sup ( A ) [/math] which means [math] \left ( x_n \right ) \to s = Sup ( A ) [/math] and so [math] s \in \bar { A } ~ ~ \blacksquare [/math]
I think this is okay, but I'm not sure, anyone got any constructive feedback?
>>8060121
s can be in A though..
>>8060134
he already dealt with that case
>>8060121
try to separate the cases and don't say things like "there is nothing to prove", it doesn't sound very good. Just say if "s in A, then s in bar(A) since A included in bar(A)"
now for the other case, you say nothing about your sequence xn.
Am I supposed to trust that any sequence of elements in A gets infinitely close to sup(A)? That sounds strange... (and it's false of course, so maybe you forget something)
try to define x_n as precisely as possible.
For example, x_n = s-1/n. Or at least something like "there exists at least one real number between s-1/n and s, choose x_n in that interval".
By the way, is A an interval? Because that previous statement is not trivial otherwise...
For example, if A is the intersection of R\Q and [0,1[ (0 included, 1 excluded), it can be a bit harder.
Try to think of all the doubts you could have while reading your proof. If you want more feedback, try rewriting it now, it will probably be much better already!
>>8060207
>he already dealt with that case
if [math]s \in A[/math] his proposition is wrong. There are sets such that [math]s = \sup A[/math], and [math]s \in A[/math]. [math] \bar A[/math] is the compliment of [math]A[/math], not the set of upper bounds of [math]A[/math]. The way his proposition is now, it does make any sense.
>>8060281
*doesn't make any sense
>>8060121
Use \sup for [math] \sup [/math]
Is [math] \bar{A} [/math] the closure of A?
>>8060281
In some situations, [math]\bar{A}[/math] denotes the closure of [math]A[/math]. Pic related, it is page 35 of baby Rudin.
>>8060281
A bar is the close of A in topology anon
Now I understand why it looks confusing
how can i prove that if [math]\langle G, * \rangle[/math] is a finite group, for any [math]a \in G, \exists n \in \mathbb{Z}^{+}, s.t. a^{n} = e[/math] ??
>>8060295
Look at the subgroup generated by a.
>>8060295
There's a few theorems that make this a one liner, but I'm going to avoid those. I'll just give you the idea. Let [math]a \in G[/math]. Then [math]a^2 \in G[/math]. Is [math]a^2 = e[/math]? If yes, then it's over, but if not, then look at [math]a^3[/math], and repeat. You will eventually reach the identity element.
Can anyone identify how I'm supposed to turn [math]1/(x+1)^2[/math] into series notation?
>>8060308
What's wrong with Taylor series?
>>8060306
i wrote this on the exam and it was marked 2 points off.. is there a principle/theorem of finite groups she might have wanted mentioned in the proof to give full credit? she is usually pretty lenient with grading so i dont know why itd be wrong
>>8060327
i just ended up using a modified geometric series
>>8060304
so would saying something like:
If [math]\langle a \rangle \neq G[/math], and [math]a \in G[/math], then [math]\langle a \rangle = H[/math], which is a subgroup of [math]G[/math], and contains [math]e[/math] by the definition of a cyclic subgroup.
be a good proof? or do i have to bring up that its finite at some point
>>8060306
>You will eventually reach the identity element.
This is really the part of the argument that needs justification.
Suppose there was no n such that a^n = e.
Then, <a> < G, G must be infinite.
>>8060331
https://proofwiki.org/wiki/Order_of_Element_Divides_Order_of_Finite_Group
https://proofwiki.org/wiki/Lagrange%27s_Theorem_(Group_Theory)
>>8060295
is it even true?
what if G is the set of all exp(i*k*pi/m), with k and m being some integers? you can always use n=2*m
>>8056973
print it off, do it then input the answers after
fuck
>>8060343
i think because its finitie its true
>>8060340
so would saying, since [math]G[/math] is finite, then it has a generator [math]\langle a \rangle[/math] such that... i just dont see any theorem in the book that doesn't specifically say cyclic group. or am i missing one that says every finite group is cyclic?
>>8060356
Multiplication by a gives a homomorphism from the subgroup generated by a to itself. Since G is finite, it is not injective. Thus the kernel is nontrivial, and you're done.
>>8058425
Computing your results using a polygon is over-complicating what you're trying to do. You have a bunch of stats and you want "good" to be represented as further away from the center, so your shape gets bigger, thus more area. Instead of that, you might as well just add all the stats together.
Financial = 6.5
Autism = 5.2
Social = 2.1
Polybius = 6.6
Side projects = 3.5
Total score = 23.9
>>8060356
(e, a, b, ab) is clearly not cyclic but finite.
(Z/nZ) X (Z/mZ) is cyclic iff m and n are relatively prime for positive m and n.
>>8060357
Fuck, it's a homomorphism from the integers to the subgroup generated by a. It takes n to a^n. I shouldn't try to answer shit on my phone.
>>8058425
>>8060360
Oops, I hit "post" too soon. Anyway, then you could assign a weight to each stat based on its importance. As for "synergy" between stats, you could just add a correlation bonus... So suppose stat1 and stat2 are highly correlated. Add a bonus to your total score like:
stat1 * stat2 * 0.9
So you get an (almost) X2 effect for those two.
However you choose to do it, it boils down to about three minutes in Excel.
>>8060367
so then what principle or theory is there that says that if [math]G[/math] is a finite group, and [math]a \in G[/math], then there is some [math]n \in \mathbb{Z}^{+}[/math] such that [math]a^{n} = e[/math], where [math]e[/math] is the identity of [math]G[/math]?? is it just supposing not and showing that makes [math]G[/math] infinite?
>>8060385
** [math]\langle G, * \rangle[/math] is a finite group
>>8060343
yes, take any element of a group and multiply itself together to infinity and you get a cyclic subgroup of that group.
for instance take [math]<\mathbb{Z}_{50},+>[/math]
Any element when added to itself will either generate a proper subgroup or all of [math]<\mathbb{Z}_{50},+>[/math], and every subgroup contains identity by definition
>>8060337
depends on exactly what you're attempting to show, that's correct if you can assume the theorems regarding cyclic subgroups
this is how the proof works using purely subgroup theorems:
First consider [math]a^{1}[/math]. If this is equal to [math]e[/math], then we are done. Otherwise, we continue to take powers of [math]a[/math]. If [math]a^{n}=a[/math], then we stop and [math]a^{n-1}=e[/math]. Otherwise, we will continue to generate different elements of the set. Since the set is finite, we must eventually run through all the elements. If we never find an [math]n[/math] such that [math]a^{n}=a[/math], then [math]G[/math] is not closed, a contradiction.
I believe this works, but basically any direct proof without using subgroup theorems will look something of this type. You basically have to terminate by finding [math]a^{n}=a^{-1}[/math] for some [math]n[/math].
>>8060403
he's clearly in an intro class, he probably hasn't even defined a homomorphism.
>It could keep cycling through a few powers larger than a over and over.
Wrong. In which case you've still found your identity element because some power of a is taking another element b to itself, which means that power of a is acting as an identity for b, and it's trivial to prove that identity is unique in any group. That means such a power of a would have to have taken a^n+1 to a, which means your condition would never actually happen.
>>8056620
OP pic is a troll (and by /sci/ standards, only a 1/10 troll).
It uses dense-matrix multiplication for a sparse matrix then uses that as "evidence" that matrices are inefficient, overlooking both the fact that generic sparse-matrix multiplication is no worse than the specialised scale transformation, and the fact that the specialised scale transformation would need to be re-written to handle anything else (like, who uses matrices when you only need scale and translation?)
>>8060397
so if there is no [math]n > 1[/math] such that [math]a^{n} = a[/math], then this is proof that [math]G[/math] is not finite. or does it just show its not closed and thats where the contradiction occurs. how does it being finite relate?
>>8060415
we already assume [math]G[/math] is finite. I wrote the proof sloppy. I should have said that clearly.
>>8060409
Of course that situation never actually happens, because it's a known result, but that doesn't excuse you from having to actually show that yourself. What you had was totally handwavy.
>>8060422
Yeah, it was. I'll admit that.
>>8060425
>>8060422
So is this a solid proof then?
If [math]a^{1} = e[/math] then [math]a[/math] is the identity. If not, then since [math]\langle G, * \rangle[/math] is finite and closed, and [math]a \in G, a^{m} = a[/math] for some [math]m \in \mathbb{Z}^{+}[/math] will eventually hold true. If not, then [math]\langle G, * \rangle[/math] would not be closed and a contradiction would occur. Now let [math]n = m - 1[/math]. Since [math]a \cdot a^{n} = a, a^{n} = e[/math] must hold true. [math]\blacksquare[/math]
>>8060441
No. Since you are still new, I recommend that you put in as much detail as possible. First of all, you need to state that [math]a \in G[/math]. Just as a formality, you need to define your letters and such when you use them. Now, in the second statement, you just claimed that the result(what you are trying to prove) is true without enough reasoning, same with your contradiction claim. You really should add more sentences and details to explain why those are true.
Here's how I would do it. The idea is kind of different than everything else so far.
Let [math]G[/math] be a finite group. Let [math]a \in G[/math] be an element of the group. Consider [eqn]a, a^2, a^3, \dots, a^n, \dots.[/eqn] This sequence has infinitely many elements, and each element of the sequence must be a member of the finite group [math]G[/math]. We can conclude that there exist 2 integers [math]n_1, n_2[/math] such that [math]a^{n_1} = a^{n_2}[/math]. We right-multiply both sides by [math]a^{n_2}[/math] and get that [math]a^{n_1 - n_2} = e[/math]. Thus, [math]n_1 - n_2[/math] is the desired number.
(Note that [math]n_1 - n_2[/math] is not necessarily the order of [math]a[/math], but that's not what the question is asking for.)
why is theta this and not from 0 to -pi/2
>>8060649
what is theta
>>8056620
Try that same comparison except also include scaling, rotating, skewing, translating, etc.
For the matrix implementation, the number of operations remains the same. For the other approach it would be impossible.
>>8056620
Ok dynamic system guys
What is the difference between STATE SPACE and STATE OF THE SYSTEM?
I said that "State space trajectory refers to a plot representing the progression of the state space in time.", and I was told that " It is the progression of the state of the systems (not the state space) and it is a result of applying the network update function " (ignore the network bit, i don't think it's relevant to the question)
>>8060843
Never mind, I get it now that state space = *all* states of the system.
But then what's the difference between STATE SPACE and STATE PORTRAIT?
Any idea where I might learn to draw lab equipment like pic related (pen and paper, not cliparts)?
>>8060360
>>8060373
Yes, I did something like that in Excel, even assigning 'titles' to each metric's numerical value.
Perhaps I didn't stress it enough. It's not so much about rigour or exactitude, but about being able to visualise it in a way that motivates me more.
Think about a strategy game. What does communicate in a more visceral way that you're doing great? Statistics about your kingdom or seeing the land extension under your control in the world map, your troops marching, etc?
I have no trouble talking to my rational mind about how I'm doing. What I need is to speak to my reptilian brain in a language that it can understand. Colourful, growing irregular polygons are the weapon I want to try.
>>8060864
what the fuck is a state portrait?
>>8060890
Sort of a family of trajectories, but isn't the state space also showing the same stuff (maybe without the arrows?)
>>8060875
Just learn to draw
http://drawabox.com/
How are the 2 equivalent? The former definition says that the derivative is taken wrt TIME and the latter one shows dV/dx .. Doesn't that mean that it's wrt to x which is not time
Fuck
>>8060893
Except those figures are closer to schematics, following some rules and design conventions, not just drawing things from sight or memory.
Can someone explain to me what variance actually is in statistics? I mean what does squaring the standard deviation actually tell you?
>>8060905
I guess, but knowing how to draw takes care of that too. My gf draws my scientific diagrams and they're always beautiful and she's an artist, not trained in following rules and design conventions
>>8060906
Variance is useless, it is just an intermediary result.
A question about homeomorphisms and lipeomorphisms: if two sets are lipeomorphic does that imply they are homeomorphic? Also is lipeomorphism an equivalence relation? It looks like it should be, but I cba to get paper out to test it...
>>8060891
oh
ok I see now.
the state space is the combination of all the possible values for each variable.
take a rigid pendulum of length L, centered at (0,0), and with a mass at the end with position (x,y).
What are the possible values for x? any value from -L to +L
same for y.
The state space is [-L,L]x[-L,L]
but all the combinations are not possible.
Because the pendulum is rigid, only values of x and y such as x^2+y^2 = L^2 are possible (a circle). This circle is the state portrait.
>>8060900
that text is gibberish.
>>8060906
the same thing as the standard deviation
>>8060920
Ohhh okay gotcha thanks anon!!
How do you manage to remember all the rules for vector/matrix multiplication?
If x and y are column vectors, and X and Y are matrices, you can do all sorts of stuff like
x * y'
y' * x
X * x
x' * X
and maybe others. I always have to look up an example to remember how to do it for each case
Matrix is are good for addition
>>8056624
Study with somebody else
Study with somebody else
"But my schedule doesn't work for that"
Reschedule and study with somebody else.
You are going thousands into debt. Either quit now before the hole is deeper or restructure so you can make the investment pay off. And by restructure I mean
Study with somebody else.
>>8057190
Basically all basic algebra, it's mostly just applying that knowledge into derivatives for a majority of calc 1
>>8061002
>How do you manage to remember all the rules for vector/matrix multiplication?
You stop thinking about things in math as rules to blindly follow.
>>8061237
Thanks man now I totally remember how to do all of them!
can someone explain if the following is true/false and why?
Let [math] F = \{f | f : \mathbb{R} \to \mathbb{R} \}[/math] be the set of real-valued functions defined on the set of real numbers. Define [math]\phi : \langle F, + \rangle \to \langle \mathbb{R}, + \rangle[/math] by [math]\phi(f) = f(0)[/math]. is it true that (a) [math]\phi[/math] is one-to-one, (b) [math]\phi[/math] is onto, and (c) [math]\phi(f + g) = \phi(f) + \phi(g)[/math]
i don't think it is one-to-one or onto, but the last one i think is true...
>>8061378
Wouldn't it be onto, since F contains a constant function for every real number, and those will give you every real when evaluated at zero?
>>8061241
I can't make you actually think about why things are true.
>>8061002
>>8061002
>I always have to look up an example to remember how to do it for each case
what?
say x= (1,2), y= (3,4)
this works with any x and y, vector or matrix
if you want x times y', you just write it this way:
...3.. 4
1 a.. b
2 c.. d
and you start multiplying. a = 1*3
b=1*4
c=2*3 and so on
I'll give another example
x=
1...2
3...4
and y is a vector (5,6)
then to find x*y you just do the same thing:
.........5
.........6
1...2..(1*5+2*6)
3...4..(3*5+4*6)
do you get it? Is this even what you were asking for?
>>8060665
the bounds for the differential of theta when converted to spherical coordinates. I got it now though.
Been at the super shitty uni, people were complaining so hard you wouldn't believe (cuz so muh learning). Left and started again at ~100th in the world. Roughly twice as much informations. People bitching only a little bit less frequent.
I expected to meet more ambitious people here. It is surely more demanding, but still not like you have to spend more than 2h out of lectures daily to be an A student.
How high majority of UG students stops being delusional and self-pitying? Top50/20/10?
>>8061378
It's not injective since x->cos x and x->1 are equal to 1 when x equals 0
It is surjective since for all y in R the function x->y is equal to y when x is equal to 0 and is included in F
And for all (f,g) in F^2, phi(f+g)=(f+g)(0)=f(0)+g(0)=phi(f)+phi(g)
>>8060864
> But then what's the difference between STATE SPACE and STATE PORTRAIT?
The state space is simply the set of possible states. A state portrait is a diagram illustrating the transitions between states.
>>8056624
The latter is an addiction, and you're overstressing the former which reinforces the latter.
Go walk in the woods and leave your phone at home.
>>8057880
Those are just spherical harmonics. Schroedinger's stuff doesn't become relevant until you do actual chemistry
Prove that if [math]m|n[/math] then [math]F_m|F_n[/math] where [math]F_i[/math] denotes the [math]i^{th}[/math] Fibonacci number.
Any really neat, cool proofs of this? Induction is simple but it's kind of long and ugly.
>>8063100
I can only offer another inductive proof.
First show by induction that [math]F_n = F_{k+1} F_{n-k} + F_k F_{n-k-1}[/math].
It's just a matter of expanding out [math]F_n = F_{n-1} + F_{n-2}[/math] repeatedly.
Showing that [math]F_m|F_n[/math] if [math]m|n[/math] is equivalent to showing that [math]F_m|F_{a m}[/math] for some integer multiple [math]a \geq 1[/math].
This follows immediately if [math]a=1[/math].
Otherwise assume that [math]F_{a m}[/math] is divisible by [math]F_m[/math].
Then we can use the identity above to write [math]F_{(a+1) m} = F_m F_{a m+1} + F_{m-1} F_{a m}[/math].
- [math]F_m[/math] divides the first term since it is a multiple of [math]F_m[/math].
- [math]F_m[/math] divides the second term since it is a multiple of [math]F_{a m}[/math] which is divisible by [math]F_m[/math] by assumption.
Thus if [math]F_m[/math] divides [math]F_{a m}[/math] then [math]F_m[/math] also divides [math]F_{(a+1) m}[/math] and by induction [math]F_m[/math] divides [math]F_{a m}[/math] for all [math]a \geq 1[/math].
Is this logic correct?
I generate 10^9 statistical samples and observe that the 99th percentile is 9. So, there's a 1% chance of obtaining a number larger than 9 in 10^9 samples, hence there's a 0.01% chance of this occurring in 10^7 samples.
Replace the figures for whatever; it's just the general idea.
>>8063242
>I generate 10^9 statistical samples and observe that the 99th percentile is 9.
>So, there's a 1% chance of obtaining a number larger than 9 in 10^9 samples
These are not the same thing
>>8063243
I mean, I'm trying to just throw a massive amount of samples at something to try and get the implied probability from the percentile as close as possible to the true probability.
Apologise if that paragraph is garbage too. Perhaps it would help if I said that those samples are the amount of inter-event times (0.1, 0.2, 0.1, 0.4 etc) that occur before they add up to, say, 1. I'm using the exponential distribution to generate these.
>>8063248
I don't really understand what you're asking, sorry.
>>8063250
Damnit. At least I know that my original idea wasn't correct, thanks for that.
>>8056624
you have downs, sorry to hear bud.
I'm trying to build a decoder from Q into d and I've tried it like 6 times without it working properly. Any idea where I went wrong?
I created Karnaugh maps from the table and got:
>d3= ~Q2 ~Q1 ~Q0 + Q2 ~Q1 Q0
>d2= ~Q1 ~Q0 + Q2 Q1 Q0
>d1= Q2 Q0 + ~Q2 Q0
>d0= Q2 Q0 + ~Q2 ~Q1 Q0
Whenever I try to implement it it doesn't work properly and I have no fucking idea
How do I quickly learn what these words mean? Apparently our lecturer assumes we know basic electricity which I don't
>>8063324
Post code
What is the mechanism for this reaction? Initially I thought of protonation of the alkene at the carbon not connected to nitrogen, followed by attack by water to the formed carbocation and departure of the tertiary amine, but I don't see any way how to end up to the ketone with that way.
From wikipedia (https://en.wikipedia.org/wiki/Cathode):
>A cathode is the electrode from which a conventional current leaves a polarized electrical device. This definition is sometimes remembered using the mnemonic CCD for cathode current departs. A conventional current describes the direction in which positive electronic charges move.
What's important to note here is that wikipedia just stated that positive charges (i.e. cations) move away from the cathode.
Literally 4 sentences later:
>Although positively charged cations always move towards the cathode (hence their name) and negatively charged anions move away from it
---
So, which is it? Are the previous two wikipedia quotes not direct contradictions of each other?
How would one generate an algorithm in mathematica or a similar program to develop a folding inflatable structure preferably in the form of a cylinder? One example would be the Yoshimura pattern, but how would you develop it?
I worked on this for half an hour off an on, took a nap, and i'm still stuck on it. I can't figure out the step in between What i have now and the original answer.
>>8063409
Some context. This is for the area of a isosceles triangle cut through the perpendicular bisector of the base.
If I masturbate whilst programming, will it rewire my brain to love programming so that it will require no motivation to write anything? Guys?
Ok, I have no clue how to do this, but maybe I'm just dumb. Given that
[math]B(100)=4[/math],
[math]B(200)=5[/math],
[math]B(300)=6[/math]
and
[math]B(400)=7.5[/math]
furthermore
[math]B(T)=c \int_0^\infty (1-\exp \left( - \frac{4\epsilon \left[\left( \frac{\sigma}{r}\right)^{12} - \left( \frac{\sigma}{r} \right)^6 \right]}{k_b T} \right) ) r^2 dr[/math],
how do I find sigma and epsilon as good as possible? Fitting is the obvious answer, but how do I do that for a function, that is defined as an integral? Thanks.
Why the fuck can't people define all their terms they use a formula. I have to guess/suppose what [math]F[/math] and [math]G[/math] are.
>>8063352
evolutionary algorithms are a good start if you want it to be partially or fully automated. Here's a decent book for that:
http://www.springer.com/us/book/9780387221960
Bear in mind that variety is good though so search for some internet resources too.
But if you're talking about general problem solving, then this book is pretty cool:
http://www.amazon.com/How-Solve-Mathematical-Princeton-Science/dp/069116407X
From the reviews:
A Classic for Problem-Solvers
By Phil on September 16, 2001
Format: Paperback
I found Pollya's "heuristic" approach to problem-solving applicable to both mathematical and non-mathematical problems. The goal of the heuristic approach is to study (and use!) the methods and rules of discovery and invention.
Here are just some of the questions that Pollya teaches as tools:
1. What is the unknown? What is the data? What conditions does the solution need to satisfy?
2. Do you know a related problem? Look at the unknown and try to think of a familiar problem having the same or a similar unknown.
3. Can you restate the problem? Can you solve a part of the problem.
4. Can you think of other data appropriate to determine the unknown?
5. Can you check the result?
6. Can you look back and use the result or the method for some other problem?
Overall, the author provides a systematic way to creatively solve problems. This volume has withstood the test of time for nearly 50 years. I recommend it highly.
Try to ask yourself fundamental questions about what you're looking for. For example, if I was looking to compress a structure why wouldn't I just crush it? I'd test that to see if would work. The crushing would provide a set of random creases that would inefficiently compress it. So the purpose is to find something that compresses well with the least amount of folds. That could be your fitness function for the evolutionary algorithm.
>>8063462
Finding the least amount of folds that still compresses could be your fitness function that is.
>>8060900
Should say x and not time. All that thing is explaining are potential wells.
Dear /sqt/.
Call me idiot or whatever, I dont care, but I cant find proper way to separate real and imaginary parts of function:
f(x)=a/(1+(ix)^(1-n))
both a and n are semi-static (aka variables I lock at certain values at the start).
I simply can't. Please help.
In before - no, this is not some stupid homework, this is for understanding the formulas behind dielectric relaxation functions. The book I have provide final outcome without explanation what happened in between. I want to understand whats going on, but blocked myself at this problem I described.
>>8063676
call p = 1-n, it's simpler
a/(1 + (ix)^p) = (a*(1+(-ix)^p)) / (1 + x^2p)
then split this in two cases: p is either even or odd.
You will get your answer
>>8063693
Thanks a lot.
>>8063100
maybe if n=km you can write F_m as the sum of k sums related to F_n =
F_n=
[1+...+m]+[(m+1)+...+(m+m)]+...[ 1+(k-1)*m +...+m+(k-1)*m], write that as [1+...+m]*something = F_m * something
Should I do the EE meme?
I'm doing an AS at a community college right now (not EE).
I'd have to go to school for a while longer since not many classes would transfer.
>>8063878
If you are into either: Electronics equipment (design, repair, circuits), High-tier Telecomunications (Networking, Broadcasting, antennas, etc etc,) or Electrical Instalations (pretty self-explanatory) then do it.
The profile is normally choosen in the 2nd-3rd year of the career depending in what courses you choose, but at first its gonna be pure abstract Maths and Physics (at least at my uni).
>>8063349
Bump.
I'd appreciate a pointer for this; not sure where to start
I do not get it
why is the sensor model multiplied with the transition model, why does this product lead to a correct specification of the joint distribution?
All the multiplication of various elements willy nilly is one of the biggest hurdles of statistical inference to me.
Like I guess the sensor model is included as nodes in the bayesian network, with state nodes as its parents, but how come this multiplicateeverywhere-thing of nodes works out?
Is there some intuition to this?
>>8064366
calculate powers of M
protip: they are repeating after a while
another protip: taylor series for sin and cos
>>8064366
Show that M^2 = -I, then split into sum over odd and even terms.
You'll end up with cos(phi) I + sin(phi) M which is a rotation matrix.
As you may have realized M is the matrix representation of i.
is this what they want you to do?
the second order table on the left is a bit handwavy I do not know if that is how you would do it like that or if you can do it like that.
Are gravitational waves created by gravity, or are they gravity?
>>8064758
In short, they are gravity. Eistien theorized that the universe was like a fabric called space-time (im sure you have heard of it). So anyway, when two dense massive objects (in the case of the LIGO detection 2 black holes) begin to orbit eachother, they begin to get closer together. As they become closer in proximity the orbiting accelerates causing ripples in space-time aka gravity).
Studying A-Level Maths and Further Mathematics here. If I want to show what a differential equals when x=0 for example, is it acceptable to write it like
>dy/dx(0) = 3
Or should I only write it like
>f'(0) = 3 or
>y'(0) = 3
I have been doing the top one all this time.
>>8064924
it's fine
>>8064886
So how come the waves from the sun or the moon are so hard to detect in comparasin to something that happened in another galaxy? Do the gravity waves not experience the same kind of decay in power as electromagnetic radiation when traveling large distances?
Do you have any pnemonics or tricks to remember solubility rules?
>>8064513
that District of Columbia! hi-larity.
Do people really use Chernoff faces? They are interesting and a little silly at the same time.
hey /sci/ i suck ass at math and i'm working through a textbook to remedy that.
one question involves a transition matrix and a state matrix, and i'd like to find the steady state using a system of equations. I have no idea how to model this given two matrices.
>>8064953
image for context.
how would i go about simplifying this?
[math]\big( f(x) \geq f(y) \or f(y) \geq f(z) \big) \and \big( f(x) \leq f(y) \or f(y) \leq f(z) \big)[/math]
>>8064992
[math]\big( f(x) \geq f(y) \vee f(y) \geq f(z) \big) \wedge \big( f(x) \leq f(y) \vee f(y) \leq f(z) \big)[/math]
mean this...
is this the correct negation of the definition for a function that is strictly monotone?
[math]\exists x, y, z \in I, \\
\Big[ (x > y > z ) \wedge \big( f(x) < f(y) \vee f(y) < f(z) \big) \Big]
\\ \wedge \\
\Big[ (x < y < z ) \wedge \big( f(x) > f(y) \vee f(y) > f(z) \big) \Big] [/math]
>>8065131
Split it in three
>>8065169
so,
[math]
a = (x > y > z) \\
b = f(x) < f(y) \\
c = f(y) < f(z) \\
[a \wedge (b \vee c) \equiv (a \wedge b) \vee (a \wedge c) ]
[/math]
is that what you mean?
Can the one-dimensional heat equation be written as
[eqn]\frac{∂y}{∂x_1} = k \frac{∂^{2}y}{∂x_2^2}[/eqn]
>>8057839
Could you also just show that the inverse function is defined for all [math]\mathbf{R}^{+}[/math]?
>>8065246
>1 dimension
>3 variables
>>8065251
>1 time variable
>1 dimension variable
>1 dependent variable
Not seeing the problem here.
>>8065253
isnt time a dimension in that context?
can someone help me prove this?
any leads would be great, im supposed to decompose the vectors and replace them until i get the proper conclusion, but i can't manage to do it
>>8065310
Well for the first 2, the dot product is defined as the magnitudes of the vectors in the same direction multiplied by each other, or total magnitudes of the vectors multiplied by each other times the cosine of the angle between them. Since they are at right angles with respect to each other, none of their magnitudes lie in the same direction, or see it as the cosine of pi/2 is 0.
For the bottom line, that's the simple result of the Pythagorean Theorem. Not sure how formal you want the proof but those are the ideas you have to convey
>>8065246
Yes, x_1 is time and x_2 is position.
>>8056620
So in a standard intro to Abstract Algebra, one would study groups, rings, fields, and Galois theory.
What few major topics does one tackle in a first course on algebraic geometry?
I ask because I'd like to skim some wiki articles before diving in too hard.
I know I could skim the table of contents on one of the canonical texts, but I was hoping to get some tips of what to focus on from an anon who has taken some AG already.
>>8065297
Since when?
One of the questions from the Euler project is find the sum of all multiples of three and five under 100.
I wrote out the first few terms to see if there was a recursive or explicit formula, but I didn't see it.
How does one do this?
[math](a \vee b) \vee (c \vee d) \equiv a \vee b \vee c \vee d[/math]
right?
>>8065380
can you count the multiples of 3 below a certain number (eg 100)?
can you do the same with 5?
if you add those two, you will be counting multiples of 15 twice each.
But you can also count the number of multiples of 15 below 100.
multiples of 3 + multiples of 5 - multiples of 15
>>8065380
one of the questions on the Euler project is to write out FizzBuzz by hand?
>>8065427
no.
>>8065427
>>8065476
OR, AND, alongside the EQUIVALENCE operators are all associative. this is basic in propositional logic. the other poster might be upset that the right hand side assumes this associativity, as in it's not well-posed for a general operator. Since OR is associative, there is not ambiguity in this form.
Need help, can someone go through this inductive proof problem with me?
Use induction to prove that if n is an integer greater than or equal to 1, then n^2 + n is divisible by 2. (lets call this function p(n))
here's what I get so far;
ya do the basis step, p(1) = true, divisible by 2.
and ur trying to prove p(n+1);
p(n+1) = (n+1)^2 + (k+1)
since p(n+1) = p(n);
(n+1)^2 + (k+1) = n^2 + n
those last three steps are were I get confused, how do I simplify this to get a proof?
>>8065511
>p(n+1)=p(nz)
this is not true, and not what the inductive step is trying to prove.
p(2) = 6 != p(1) = 2. both are divisible by 2, though.
The inductive step is assume it's true for the case of n, and then show that it follows the proposition is also true for the case of n+1.
Assume n^2 + n is divisible by 2 and then show that this implies (n+1)^2 + (n+1) is divisible by 2.
Those last three steps confused you because they were absolutely incorrect.
>>8065511
I don't think you get how this works, but it's fine, that's why you asked.
Do you understand the basic principle? Induction is like a ladder. To climb the ladder, you need two things: the ability to climb the first step, and assuming you are on a certain step, the ability to climb to the next one.
Try to write the induction properly please, you will only get better if you make that extra effort.
in your case. let's call p(n) the fact that n^2+n is divisible by 2
your proof needs to go like this:
i) initialization: 1^2+1=2, so p(1) is true.
ii) induction or whatever you want to call it:
ASSUME p(n) is true for a certain value of n. That means assume n^2+n is divisible by 2 for some value of n.
You need to prove that if this is true, then p(n+1) is true as well, that is (n+1)^2+(n+1) is also divisible by 2.
NOWHERE can you write p(n+1)=p(n). NOWHERE can you write p(n+1)=(n+1)^2+(n+1).
p(n) is a property, not a number.
Can you do this?
>>8065551
try googling proof by induction and how to use the 'inductive step.' you're missing the general idea.
use what-you know (assumed in the inductive step) to show what you expanded is divisible by 2.
>>8065551
>is the next step I want to get
>(n+1)^2 + (n+1) = n^2 +2n +1 + n +1
no you don't want to get that. That's a fact, you won't get cookies for writing this.
So starting from (n+1)^2+(n+1) = n^2+3n+2, and using the fact that n^2+n is even, can you prove n^2+3n+2 is even?
That's where you get your marks.
>>8065562
ok here, lets try this (thank you for helping, btw)
p(n) = n^2+n is divisible by 2
i) Basis step: 1^2+1=2, so p(1) is true.
ii)induction:
Assume true for n = k
k^2 + k is divisible by 2
prove p(k+2) holds true, is divisible by 2.
(k+1)^2 + (k+1)
k^2 + k + k + 1 + k + 1
k^2 + 2k+1+ k + 1
k^2 + 2k + k + 2
k^2 + k + 2k + 2
K^2 + k is divisible by 2, 2k is divisible by 2, 2 is divisible by 2
>>8065588
that's better, polite sage
>>8065624
>polite sage
is this guy for real
>>8065588
much better indeed
>Assume true for n = k
just say assume it is true for some n>=1 (or some k>=1).
all the rest is good
Don't forget at the end to say "therefore p(k+1) is true", because that's what you needed to show in the second step
Ok guys, I'll be neet for 10 moths. What should I learn and why.
My background is multivariable calculus, linear algebra and ODE.
This one looks simple, but I just don't know how to do it. Please help
TAC is 35N and I need to find alpha and TBC
>>8063349
Well inside the capacitor, charges move from the anode to the cathode, then they leave the cathode
What are the most important / versatile classes for applied mathematics? PDEs? ODEs? Stochastic processes? Numerical Methods?
I'm thinking of a career in high performance scientific computing, numerical modeling and stuff like that. I can dig into the specifics for whichever area I want to investigate, but I know the math should be similar regardless of application area.
Not exactly sure which classes to choose from. I mean from a numerical standpoint I don't think something like real analysis would be particularly relevant since it seems too analytic.
If I pair this shit with parallel programming, operating systems, FPGAs, networking and distributed algorithms, would that make a good elective selection? Or am I missing something more important?
>>8065745
finite elements.
>>8065745
courses from the math department
-proofs
-analysis advanced calculus
-pde
-non linear ode
-complex variables
-numerical analysis
-linear programming
-stats/probability
more direct courses from the eng. or physics department if you do not want the rigor of the math department
-numerical methods for engineers
-mathematical methods
-stats/probability
most of the math needed in the real world can be found in a book like this, and taught in a one year sequence usually taught by the physics department.
http://www.amazon.com/dp/0521679710/ref=pd_lpo_sbs_dp_ss_3/183-3819061-0512617
>>8065745
Depends on your discipline, numerical methods and FDM/FEM is the most general you can do for undergrad, but you won't be able to into depth in it anyway.
>>8065738
I can tell you that B is going to be a LOT further away than the picture would seem to indicate.
>>8065776
Wow. That's a really cool book. I'll look into it thanks!
But yeah, I can't register for many pure classes due to departmental restrictions, so applied / engineering math seems the way to go.
Either way, I still think I'll have an edge over the pure people when it comes to jobs or research since I'll have algorithms and parallel programming experience to crunch numbers harder.
>>8065786
I'm in computer engineering but I'll finish in two years and have the last two years to take whatever electives I can get my hands on. I may or may not be able to get into grad classes by junior year to get into something very detailed, which is why I'm asking for the broad fundamentals.
What do you guys think about optimization?
>>8065801
Nevermind, you mentioned linear programming.
>>8065776
that's the book we use at imperial for engineering, the problems in there are really good.
>>8065807
Ayy, I got in there but mistakenly chose ChemE which was pretty dead end for a chink such as myself.
Don't know why Americlaps don't make books as comprehensive as that.
I don't know, but when I was under the British system (A Levels, etc) everything seemed much more organized.
Nothing in the US seems standardized, from high school to university. Makes everything really complicated imo
>>8064930
To cause detectable distortions in space time VERY dense objects are needed. Just as you don't feel strong gravitational force (comparable to orbiting planets or the force of g keeping us bound to the surface of earth) between two people, solar mass objects don't create very strong gravitational waves.
>>8057827
great lecture, thanks anon
>>8065801
>What do you guys think about optimization?
That and numerical methods/analysis
If you like controls complex variables.
keep in mind there is a difference between numerical analysis and numerical methods
numerical analysis full year sequence covering how and why an algorithm works taught by the math department
http://www.amazon.com/Numerical-Analysis-2nd-Timothy-Sauer/dp/0321783670
numerical methods one semester/quarter how an algorithm works taught by the engineering department
http://www.amazon.com/Numerical-Methods-Engineers-Scientists-Gilat/dp/1118554930
>>8065812
this book is excellent but does not have a solution manual for self study hence why the uk riley is popular
http://www.amazon.com/Advanced-Engineering-Mathematics-Michael-Greenberg/dp/0133214311
when you finish the basic math methods type books this one is good grad level book
www.amazon.com/Advanced-Mathematical-Methods-Scientists-Engineers/dp/0387989315/
>>8065776
The description doesn't say what topics it actually covers?
>>8065829
My school uses a semester system so I don't think I can afford to waste an entire semester on just complex variables, especially since I would already have exposure from other classes.
>>8065861
Hmm that's weird. In my school apparently its "numerical methods" that is the full year course, whereas "numerical analysis" is one semester.
http://scicomp.cs.illinois.edu/courses.html
>this book is excellent but does not have a solution manual for self study
Why do people do this? Many of my professors are extremely anal about giving out the solutions manuals to books they authored themselves. Something about them diminishing the challenge or something, even if you try to convince them you're disciplined in using them, they still refuse.
>>8065889
You know, at first I was convinced by the whole "you don't need to know if your answer is correct" meme, but after working as TA I quickly realized that professors are just lazy in structuring their exam questions. So students having a solution manual would mean they'd have to put some effort into coming up with creative questions for once.
>>8065917
I mean its literally useless to practice on questions that you can't even get the answers to. You'd walk away not knowing if your entire line of reasoning was correct or not, and if you walk away thinking you're right you'd just risk developing incorrect thought patterns and assumptions.
>b-but muh open ended research problems
>in academia nobody has the answers
Well its not like you're gonna open endedly grade my exam right?
Sheesh
>>8065889
odd naming conventions
where i went math 170 abc is numerical analysis
math 171 ab is linear programming or numerical optimization
https://www.ucsd.edu/catalog/courses/MATH.html
mae 107 is one quarter of numerical methods for engineers
also our mae department teaches their own applied version of pde mae 105
http://www.ucsd.edu/catalog/courses/MAE.html
the structural engineers have their own numerical methods course se 102
http://ucsd.edu/catalog/courses/SE.html
>>8065955
I wouldn't say it's entirely useless, but yes especially what you said about risk for developing incorrect thought patterns and assumptions is worrying.
In the end it's just a waste of time when. There are plenty of actual open ended design problems to keep you intelectually stimulated and teach you how to revise your own work. Professors shouldn't be fucking with your fundamentals by refusing to give you answers.
Why don't we use "heterogeneous" to describe a differential equation that isn't homogeneous?
>>8065986
we do
>>8066020
I dunno, I've only ever seen or heard "nonhomogeneous" or "inhomogeneous".
>>8065511
P(n)=n^2+n.
P(1)=2 is even.
Assume P(n-1) is even. Then P(n)=n*(n+1) is even because one factor on the right is even. Silly problem.
Why is it called integration and differentiation?
